The Yang-Baxter Equation, (Quantum) Computers and Unifying Theories

Abstract

Quantum mechanics has had an important influence on building computers;nowadays, quantum mechanics principles are used for the processing and transmission ofinformation. The Yang-Baxter equation is related to the universal gates from quantumcomputing and it realizes a unification of certain non-associative structures. Unifyingstructures could be seen as structures which comprise the information contained in other(algebraic) structures. Recently, we gave the axioms of a structure which unifies associativealgebras, Lie algebras and Jordan algebras. Our paper is a review and a continuation of thatapproach. It also contains several geometric considerations.

Keywords

• universal gate
• quantum computer
• Yang-Baxter equation
• Jordan algebras
• Lie algebras
• associative algebras